We present selected results of observations and monitoring of cataclysmic variables (CVs) and related objects by the instruments IBIS and OMC onboard INTEGRAL. We analyse the behaviour of the intermediate polar (IP) V1223 Sgr in a state which we call a shallow low state. We present far X-ray spectra ($E$ up to 60 keV), and the optical and far X-ray orbital modulation. The relation between far X-ray and optical flux appears to be stable over about 400 days. We also present far X-ray observations of some other CVs (or at least upper limits of their far X-ray fluxes) and show that the systems with magnetized white dwarf (like polars and IPs) are observable with INTEGRAL. The OMC light curves show that an outburst and a shallow low state of IX Vel are caused by the mass transfer variations, and not by the thermal instability of the disk, and that the amplitude of the flickering decreases with the decreasing intensity of the “stable” component.